'Ring a Ring of Numbers' printed from http://nrich.maths.org/

Oli from Oakmeeds School began the first part of this question where we had to make odd differences between pairs of numbers.

You need odd, even, odd, even as odd + even make odd. Each
pair has an odd and an even.

Rukmini from Hopscotch Nursery also said:

When the differences are all odd, the sums are all odd.
Rukmini then went on to say:

To make the differences even, you need the numbers 2, 4, 6, 8. Then the
sums are also even.
Absolutely right - well done to both Oli and Rukmini. What about the order of the numbers 2, 4, 6 and 8 in the ring? Does it matter? I'll leave you all to ponder on that.